Question

1. if mo bisects ∠pmn, m∠pmn = 74° and m∠omn=(2x + 7)°, find the value of x.

Explanation:

Step1: Recall angle - bisector property

Since $\overrightarrow{MO}$ bisects $\angle PMN$, then $m\angle PMO=m\angle OMN$. And $m\angle PMN = 74^{\circ}$, so $m\angle OMN=\frac{1}{2}m\angle PMN$. Thus $m\angle OMN = 37^{\circ}$.

Step2: Set up an equation

We are given that $m\angle OMN=(2x + 7)^{\circ}$. So we set up the equation $2x+7 = 37$.

Step3: Solve the equation for x

Subtract 7 from both sides of the equation: $2x=37 - 7=30$. Then divide both sides by 2: $x=\frac{30}{2}=15$.

Answer:

$x = 15$